First, Driver id is not selected in your top query to group by.
Second Driver Id I believe needs to have a group by in all of your sub
queries
Third, I think you actually want to sum the top level, not count

SELECT Sum(Expr1) AS Expr1, [Driver ID]
FROM
(
SELECT Count(*) AS Expr1, [Driver ID]
FROM [Current Jobs]
WHERE ((([Date]) Between [From Date] And [To Date]))
GROUP BY [Driver ID]

UNION ALL
SELECT COUNT(*) AS Expr1, [Driver ID]
FROM [Bookings]
WHERE ((([Date]) Between [From Date] And [To Date]))
GROUP BY [Driver ID]

UNION ALL
SELECT COUNT(*) AS Expr1, [Driver ID]
FROM [Contract Jobs]
WHERE ((([Date]) Between [From Date] And [To Date]))
GROUP BY [Driver ID]
)
GROUP BY [Driver ID]
ORDER BY [Driver ID];